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a) $\frac{{14}}{{18}}:\frac{8}{9} = \frac{7}{9}:\frac{8}{9} = \frac{7}{9} \times \frac{9}{8} = \frac{{63}}{{72}} = \frac{7}{8}$
b) $\frac{9}{6}:\frac{3}{{10}} = \frac{3}{2}:\frac{3}{{10}} = \frac{3}{2} \times \frac{{10}}{3} = \frac{{30}}{6} = 5$
c) $\frac{4}{5}:\frac{{10}}{{15}} = \frac{4}{5}:\frac{2}{3} = \frac{4}{5} \times \frac{3}{2} = \frac{{12}}{{10}} = \frac{6}{5}$
d) $\frac{1}{6}:\frac{{21}}{9} = \frac{1}{6}:\frac{7}{3} = \frac{1}{6} \times \frac{3}{7} = \frac{3}{{42}} = \frac{1}{{14}}$
\(1-\left(\frac{12}{5}+y=\frac{8}{9}\right):\frac{16}{9}=0\)
\(1-\left(\frac{12}{5}+y-\frac{8}{9}\right)=0\times\frac{16}{9}\)
\(1-\left(\frac{12}{5}+y-\frac{8}{9}\right)=0\)
\(\frac{12}{5}+y-\frac{8}{9}=1-0\)
\(\frac{12}{5}-y+\frac{8}{9}=1\)
\(\frac{12}{5}-y=1-\frac{8}{9}\)
\(\frac{12}{5}-y=\frac{1}{9}\)
\(y=\frac{12}{5}-\frac{1}{9}\)
\(y=\frac{108}{45}-\frac{5}{45}\)
\(y=\frac{103}{45}\)
a) \(\left(\frac{5}{12}+\frac{1}{4}\right)\cdot\frac{6}{4}=\left(\frac{5}{12}+\frac{3}{12}\right)\cdot\frac{3}{2}=\frac{8}{12}\cdot\frac{3}{2}\)\(=\frac{24}{24}=1\)
b) \(\left(\frac{5}{3}-\frac{7}{6}\right):\frac{2}{5}=\left(\frac{10}{6}-\frac{7}{6}\right):\frac{2}{5}=\frac{3}{6}:\frac{2}{5}\)\(=\frac{1}{2}:\frac{2}{5}=\frac{5}{4}\)
a.(5/12+1/4)+6/4
=(5/12+3/12)+6/4
=8/12+6/4
=8/12+18/12
=20/12
=5/3
b.(5/3-7/6):2/5
=(30/18-21/18):2/5
=9/18:2/5
=1/2:2/5
=1/2*5/2
=5/4
\(a.\frac{3}{7}.\frac{5}{6}+\frac{5}{6}.\frac{4}{7}=\left(\frac{3}{7}+\frac{4}{7}\right).\frac{5}{6}=1.\frac{5}{6}=\frac{5}{6}\)
\(b.\frac{1}{6}:\frac{4}{5}+\frac{1}{8}:\frac{4}{5}=\left(\frac{1}{6}+\frac{1}{8}\right):\frac{4}{5}=\left(\frac{4}{24}+\frac{3}{24}\right):\frac{4}{5}=\frac{7}{24}:\frac{4}{5}=\frac{7.5}{24.4}\)\(=\frac{35}{96}\)
\(c.\frac{1}{6}:\frac{4}{5}-\frac{1}{8}:\frac{4}{5}=\left(\frac{1}{6}-\frac{1}{8}\right):\frac{4}{5}=\left(\frac{4}{24}-\frac{3}{24}\right):\frac{4}{5}\)\(=\frac{1}{24}:\frac{4}{5}=\frac{1.5}{24.4}=\frac{5}{96}\)
a) \(\frac{3}{7}\cdot\frac{5}{6}+\frac{5}{6}\cdot\frac{4}{7}\)
\(=\left(\frac{3}{7}+\frac{4}{7}\right)\cdot\frac{5}{6}\)
\(=1\cdot\frac{5}{6}\)
\(=\frac{5}{6}\)
b) \(\frac{1}{6}:\frac{4}{5}+\frac{1}{8}:\frac{4}{5}\)
\(=\left(\frac{1}{6}+\frac{1}{8}\right):\frac{4}{5}\)
\(=\frac{7}{24}:\frac{4}{5}\)
\(=\frac{35}{96}\)
c) \(\frac{1}{6}:\frac{4}{5}-\frac{1}{8}:\frac{4}{5}\)
\(=\left(\frac{1}{6}-\frac{1}{8}\right):\frac{4}{5}\)
\(=\frac{1}{24}:\frac{4}{5}\)
\(=\frac{5}{96}\)
\(\frac{1}{2}:\frac{3}{2}:\frac{5}{4}:\frac{6}{5}:\frac{7}{6}:\frac{8}{7}\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\)
\(=\frac{1\cdot\left(2\cdot5\cdot6\cdot7\right)}{8\cdot3\cdot\left(2\cdot5\cdot6\cdot7\right)}\)
\(=\frac{1}{24}\)
\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\cdot\frac{8}{9}\cdot\frac{9}{10}\)
\(=\frac{1\cdot\left(2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\right)}{\left(2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\right)\cdot10}\)
\(=\frac{1}{10}\)
\(1.a,\frac{5}{7}=\frac{5.9}{7.9}=\frac{45}{63};\frac{4}{9}=\frac{4.7}{9.7}=\frac{28}{63}.\)
\(b,\frac{7}{15},\frac{5}{3}=\frac{5.5}{3.5}=\frac{25}{15}\)
\(c,\frac{11}{12}=\frac{11.4}{12.4}=\frac{44}{48};\frac{7}{48}\)
\(d,\frac{3}{2}=\frac{3.3}{2.3}=\frac{9}{6};\frac{2}{3}=\frac{2.2}{3.2}=\frac{4}{6}\)
\(e,\frac{1}{3}=\frac{1.4}{3.4}=\frac{4}{12};\frac{5}{4}=\frac{5.3}{4.3}=\frac{15}{12};\frac{10}{12}\)
a: =6x5/4=30/4=15/2
b: =8x7/12=56/12=14/3
c: =5x8/7=40/7
d: =15x3/5=9
a: =6x5/4=30/4=15/2
b: =8x7/12=56/12=14/3
c: =5x8/7=40/7
d: =15x3/5=9